On divergence form SPDEs with VMO coefficients [PDF]
arXiv, 2008 We present several results on solvability in Sobolev spaces $W^{1}_{p}$ of SPDEs in divergence form in the whole space.
arxiv
An almost sure energy inequality for Markov solutions to the 3D Navier-Stokes equations [PDF]
arXiv, 2009 We prove existence of weak martingale solutions satisfying an almost sure version of the energy inequality and which constitute a (almost sure) Markov process.
arxiv
Generalized backward doubly stochastic differential equations driven by Lévy processes with non-Lipschitz coefficients [PDF]
arXiv, 2009 We prove an existence and uniqueness result for generalized backward doubly stochastic differential equations driven by L\'evy processes with non-Lipschitz assumptions.
arxiv
Stochastic differential equation modelling of cancer cell migration and tissue invasion. [PDF]
J Math Biol, 2023 Katsaounis D +2 more
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Ergodicity of infinite white $α$-stable Systems with linear and bounded interactions [PDF]
arXiv, 2009 We proved the existence of an infinite dimensional stochastic system driven by white $\alpha$-stable noises ($1<\alpha \leq 2$), and prove this system is strongly mixing. Our method is by perturbing Ornstein-Uhlenbeck $\alpha$-stable processes.
arxiv
Model problem for integro-differential Zakai equation with discontinuous observation processes in Hölder spaces [PDF]
arXiv, 2010 The existence and uniqueness of solutions of the Cauchy problem to a a stochastic parabolic integro-differential equation is investigated. The equattion considered arises in nonlinear filtering problem with a jump signal process and jump observation.
arxiv
Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise. [PDF]
Stoch Partial Differ Equ, 2023 Fahim K, Hausenblas E, Kovács M.
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On a space discretization scheme for the Fractional Stochastic Heat Equations [PDF]
arXiv, 2011 In this work, we introduce a new discretization to the fractional Laplacian and use it to elaborate an approximation scheme for fractional heat equations perturbed by a multiplicative cylindrical white noise. In particular, we estimate the rate of convergence.
arxiv
Invariance measures of stochastic 2D Navier-Stokes equations driven by $α$-stable processes [PDF]
arXiv, 2011 In this note we prove the well-posedness for stochastic 2D Navier-Stokes equation driven by general L\'evy processes (in particular, $\alpha$-stable processes), and obtain the existence of invariant measures.
arxiv
Raman Spectroscopic and Quantum Chemical Investigation of the Pyridine-Borane Complex and the Effects of Dative Bonding on the Normal Modes of Pyridine. [PDF]
ACS Omega, 2022 Lambert EC, Stratton BW, Hammer NI.
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